A sum of money was distributed equally in a class of boys. Had there been 10 boys more, each would have received a rupee less. If there had been 15 boys less, each would have received 3 rupees more. Find the sum of money and the number of boys.

# A sum of money was distributed equally in a class of boys. Had there been 10 boys more, each would have received a rupee less. If there had been 15 boys less, each would have received 3 rupees more. Find the sum of money and the number of boys.

1. A
Rs.300
2. B
Rs.200
3. C
Rs.500
4. D
Rs.700

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### Solution:

Let the number of boys beand the total sum of money berupees.
Sum of money received by each boy
Here, the number of boys becomes .
Sum of money received by each boy
The sum of money received by each boy (where the number of boys is ) is Re. 1 less than the sum of money received by each boy (where the number of boys is ).
Therefore, we get the equation

Simplifying by cross multiplication, we get

Multiplying by using the distributive law of multiplication, we get

Subtracting  from both sides, we get

Rewriting the equation, we get

Sum of money received by each boy
The sum of money received by each boy (where the number of boys is ) is Re. 1 less than the sum of money received by each boy (where the number of boys is ).
Therefore, we get the equation

Simplifying by cross multiplication, we get

Multiplying by using the distributive law of multiplication, we get

Subtracting  from both sides, we get

Dividing both sides by 3 and rewriting the equation, we get

Subtracting equation from equation , we get

Adding and subtracting the like terms, we get

Dividing both sides by 5, we get

Substituting  in the equation ,we get

Subtracting from both sides, we get

Thus, the number of boys is 40.
Substitutingin the equation , we get

The total sum of money is Rs. 200.
So, option 2 is correct.

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